Equation Basepoint Parameter Dimension Restrictions of Isotropy #1 W = XY + Z (0, 0, 0, 0) 4 #2 W 2 = XY + Z + 1 (1, 0, 0, 0) 3 #3 W = XY + Z +X (0, 0, 0, 0) 2 #4 W = XY + Z +XZ + αX (0, 0, 0, 0) α arbitrary 1 #5 W = XY + Z +XZ (0, 0, 0, 0) 1 #6 W 2 = XY +XY +XZ (1, 1, 0, 1) 1 #7 W = XY + Z (1, 0, 0, 1) α 6= 0, 1, 2 1 #8 W = XY + e (1, 0, 0, 0) 1 #9 W = XY + logZ (0, 0, 0, 1) 1 #10 W = XY + Z l...

3 ABSTRACT C57BL/6J (B6) mice containing the Mus domesticus poschiavinus Y chromosome, Y

Abstract. Definitions from the theory of point processes are recalled. Models of intensity function paramaterization and maximum likelihood estimation from data are explored. Closed-form log-likelihood expressions are given for the Hawkes (unidimensional andmultidimensional)process, Autoregressive Conditional Duration(ACD), and Log-ACD models. The Autoregressive Conditional Intensity model is a...

We discuss some recent determinations of the equation of state for the XY and the Heisenberg universality class.

for entire functions, the notions of their growth indicators such as ritt order are classical in complex analysis. but the concepts of relative ritt order of entire functions and as well as their technical advantages of not comparing with the growths of $exp exp z$ are not at all known to the researchers of this area. therefore the studies of the growths of entire functions in the light of thei...

abstract the spontaneous emission spectrum from a driven three-level atom placed inside a double-band photonic crystal has been investigated. we use the model which assumes the upper levels of the atomic transition are coupled via a classical driving field. the transition from one of the upper levels to lower level couples to the modes of the modified reservoir, and the transition from the othe...

This curve has the points (1 : 0 : 0) and (0 : 1 : 0) at infinity over any field. The affine equation is XY +Y +X = 0. The origin is a point of this curve. If (x, y) ∈ F8 is a point of this curve with nonzero coordinates, then x = 1. So 0 = xy + y + x = xy + xy + x = x[(xy) + (xy) + 1]. Let t = xy. Then t + t+ 1 = 0. So the Klein quartic has 3.7 = 21 rational points over F8 with nonzero coordin...

The method of moments is used to investigate the spin dynamics of paramagnetic EuO and EuS. The theory predicts correctly those wavevectors for which a ‘spin wave’ peak appears in the spectrum. Furthermore the calculated position of this peak, when one occurs, agrees well with experiment. This suggests that earlier work, in which the same method was applied to an effective Heisenberg model for ...

The singular values of XY − Y X are the objects under investigation. Here, X and Y are square matrices with complex entries, and one of them has rank one. Hence, there are at most two non-trivial numbers among the commutator’s singular values, and the pairs of interest can be depicted in the plane. The emphasis will lie on the unexpectedly intriguing case in which both matrices are of rank one ...

S. J. Mitchell, M. A. Novotny, José D. Muñoz Center for Materials Research and Technology and Department of Physics, Florida State University, Tallahassee, Florida 32306-4351, USA Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4130, USA Institute for Computer Applications 1, University of Stuttgart, D-70569 Stuttgart, Germany Permanent addres...